Question

Probability
Class 10
Please answer question no.3 and 4.​

Answer 1

Answer:

3. No. of black balls = x

Total no. of balls = 12

The probability that the ball will be black = x/12

Now, the no. of black balls = 6+x

Probability is given = 2(x/12) = x/6

But the probability should be = 6+x/12

so, x/6 = 6+x/12

     x/6 - x/12 = 6

2x-x/12 = 6

x = 6X12

x = 72

4. Let the no. of green marbles = x

and, no. of blue marbles = y

Total marbles given are = 24

So, x+y=24 -----1.

And, Probability that the marble will be green = 2/3

But the probability is given by = x/24

So, 2/3 = x/24

2X24/3 = x

16 = x

Putting the value of x in 1.

16+y = 24

y = 24-16

y = 8

So the blue marbles are 8

Step-by-step explanation:

Hope it helps you mate :)

Answer 2

QUESTION 1:

A box contains 12 balls of which x are black . If one is drawn at random from the box, what is the probability that it will be a black ball ? If 6 more black balls are put in the box, the probability of drawing a black ball now is double of what it was before. Find x.

ANNSWER:

• The value of x = 3

GIVEN:

• A box contains 12 balls.

• x balls are black.

• When 6 more black balls are added, the probability of drawing a black ball will be doubled.

EXPLANATION:

Let B be the event of getting a black ball

P(B) = n(B) / n(S)

n(B) = x

n(S) = 12

p(A) = x / 12

when 6 black balls are added

n(S) = 12 + 6 = 18

n(B) = x + 6

Let the new probability be P(A)

P(A) = (x + 6) ÷ 18

P(A) = 2P(B)

(x + 6) ÷ 18 = 2(x / 12)

(x + 6) ÷ 18 = x / 6

(x + 6) ÷ 3 = x

x + 6 = 3x

2x = 6

x = 3

HENCE THE VALUE OF X = 3

VERIFICATION:

P(B) = 3 / 12 = 1 / 4

P(A) = (3 + 6) ÷ 18 = 9 / 18 = 1 / 2

1 / 2 = 2(1 / 4)

1 / 2 = 1 / 2

P(A) = 2P(B)

HENCE VERIFIED

QUESTION 2:

A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/3. Find the number of blue balls in the jar.

ANSWER:

• Number of blue balls = 8

GIVEN:

• A jar contains 24 marbles.

• Probability of taking a green marble = 2/3

EXPLANATION:

Let B be the event of getting a blue marble and G be the event of getting a green marble.

P(B ∪ G) = P(B) + P(G) - P(B ∩ G)

P(B ∩ G) = 0 [ Because no marbles will have both the colours ]

P(B ∪ G) = 1 [ P(B ∪ G) = n(S) / n(S) = 1 ]

P(G) = 2/3

1 = P(B) + 2/3 - 0

P(B) = 1 - 2/3

P(B) = 1/3

P(B) = n(B) / n(S)

P(B) = 1/3

n(S) = 24

1/3 = n(B) / 24

24/3 = n(B)

n(B) = 8

HENCE THE NUMBER OF BLUE BALLS = 8